The problem of reliable data delivery at low energy cost arises as one of the most challenging research topics in underwater wireless sensor networks (UWSNs). Reliable data delivery is demanding because of the acoustic channel impairments and channel fading. Moreover, it is energy hungry given the high cost of acoustic communication. In wireless ad hoc & sensor networks, separately, opportunistic routing has been employed to improve data delivery whereas duty cycled operation mode has been adopted to achieve energy efficiency and prolonging network lifetime. In this paper, we investigate the benefits and drawbacks of collision between opportunistic routing paradigm and duty cycle techniques in UWSNs. We propose an analytical model to study and evaluate the performance of opportunistic routing protocols under duty cycled settings designed from three mainly paradigms: simple asynchronous, strobed preamble and receiver initiated; and different network densities and traffic loads. The results show that while duty cycle reduces the energy consumption, it affects negatively in the opportunistic routing performance, increasing the delay and the expected number of transmissions to deliver a packet. The simple duty cycled approach is shown to be suitable for applications that require long-lived network and can tolerate some degree of packet losses. Our results indicate that strobed preamble-based duty cycle is the most effective approach to be integrated with opportunistic routing, when high fidelity monitoring is required, even having not the best performance in terms of energy savings.